Abstract
Generic short-range interacting quantum systems with a conserved quantity exhibit universal diffusive transport at late times. We employ nonequilibrium quantum field theory and semiclassical phase-space simulations to show how this universality is replaced by a more general transport process in a long-range XY spin chain at infinite temperature with couplings decaying algebraically with distance as . While diffusion is recovered for , longer-ranged couplings with give rise to effective classical Lévy flights, a random walk with step sizes drawn from a distribution with algebraic tails. We find that the space-time-dependent spin density profiles are self-similar, with scaling functions given by the stable symmetric distributions. As a consequence, for , autocorrelations show hydrodynamic tails decaying in time as and linear-response theory breaks down. Our findings can be readily verified with current trapped ion experiments.
- Received 7 September 2019
DOI:https://doi.org/10.1103/PhysRevB.101.020416
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